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\chapter{Theoretical foundations}\label{chap:Chp2} % top level followed by section, subsection

\begin{quotes}
You cannot step into the same river twice.\\
\attrib{Heraclitus quoted by Plato in Cratylus,  \citeyearpar[][Fragment 41]{sedley2003}   }
\end{quotes}



\begin{quotes}
Does Mr. Durkheim think that social reality is anything other than individuals and individual acts or facts? If you believe that \ldots I understand your method which is pure ontology. Between us is the debate between nominalism and scholastic realism. I am a nominalist. There can only be individual actions and interactions. The rest is only a metaphysical entity, mysticism \ldots Il n'y a de r\'ealit\'e que dans l'action' \\ 
\attrib{Gabriel Tarde {[}1908{]} \citeyearpar[][p 140]{tarde1969}   }
\end{quotes}


\begin{quotes}
Those who arrive at Thekla can see little of the city beyond the plank fences, the sackcloth screens, the scaffoldings, the metal armatures, the wooden catwalks hanging from ropes or supported by sawhorses, the ladders, the trestles. If you ask, `Why is Thekla's construction taking such a long time?'' the inhabitants continue hoisting sacks, lowering leaded strings, moving long brushes up and down, as they answer, `So that its destruction cannot begin.' And if asked whether they fear that, once the scaffoldings are removed, the city may begin to crumble and fall to pieces, they add hastily, in a whisper, `Not only the city.' \\
\attrib{Italo Calvino \citeyearpar[p 127]{Calvino1978}   }
\end{quotes}






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\section{Introduction}
The purpose of this chapter is to present the theoretical framework of micro-foundations, and to explore how it may contribute to the field of social networks. Micro-foundations has been increasingly attracting scholarly attention over the past decade or so \citep{demeulenaere2011} in particular in the field of organization studies \citep{felin2006,abell2008}. We might want to consider the application of micro-foundations to the field of social networks as an interesting intellectual experiment, testing the usefulness of the theory in shedding light on some of the findings established in the field.  

Another reason to consider micro-foundations stems from the common language it shares with economics. If the theory facilitates the understanding and interpretation of social network findings, one may be inclined to start thinking of the prospect for using it to pave the way for a unified social science, a bridge between economics and sociology \citep{abell2003}. 

Micro-foundations also provides a useful way of organizing and guiding empirical research, not so much thanks to its ability to make predictions about outcomes but as a way to organize social explanations and entities, judging what a social explanation needs to entail and how different explanations stand in relation to one another, complementing each other to form what one may call a grand-theory of social change \citep{boudon1986}. 

A further reason to turn to micro-foundations in the context of networks, is that this framework arguably provides a way of addressing a long standing debate in the field, the debate about the nature and essence of social ties. Various answers have been suggested to this question \citep{Borgatti2009,Podolny2001}, but common to them all is the distinction between the conceptualization of ties as durable, semi-static \textit{structures} connecting between entities and the notion of momentary action, movement or \textit{flow}. Whether structure or flow, the ontological status of ties seems to belong to one of those insoluble debates one could trace back to a famous aphorism coined in ancient Greece. I am referring here to the puzzling relationship between that which  is durable and that which is changing, between the essence of a river as a stable idea in the mind and its defining character of flowing matter (see opening quote for this chapter.) Granted that ontological questions like this will surely continue to boggle the mind, but in what follows I would like to assess the claim that micro-foundations could perhaps provide a tentative way to grapple with this question or at least represent it in a coherent manner. 

The chapter is divided into two parts: in the first part, the principles of micro-foundations are briefly demonstrated through the Coleman `boat' diagram. This diagram illustrates the distinction between different levels of social aggregation and the possible explanatory links connecting between them. To anchor the problem in a wider intellectual project, we embark on a brief excursion back to a debate between Gabriel Tarde and \'Emile Durkheim, followed by some helpful notions about social action from Marcel Mauss, Georg Simmel and Max Weber, finally reaching the very founding fathers of the field of social networks, the scholars who began speaking systematically of social networks as a model of the social. 

The second part of the chapter is an attempt to organize a few of the more famous social network findings into categories, trying to assess whether they fit into the framework of micro-foundations as interpreted through Coleman's diagram. This is where we will find some open questions regarding the links between social action and networks, questions that will guide the empirical investigation.  

\section{Coleman's boat and micro-foundations}\label{sec:colemansboat}

Coleman's \citeyearpar{coleman1990} diagram (figure \ref{ImgColemanBasic})  describes four types of social explanations, all of them derived from a basic distinction between two levels of analysis or levels of aggregation, the macro-level of the collective and the micro-level of individuals.\footnote{Some reject this distinction, claiming that there is no difference in kind between micro-level entities and macro-level ones. Granted it is true that every collective is linked with multiple individuals, but by the same token every individual is also linked with multiple collectives \citep{latour2012}. We would therefore expect some symmetry between the level of the macro and the level of the individual, a symmetry that is not apparent from Coleman's diagram. This is an important critique we shall return to in Chapter 6, discussed in light of the empirical findings.}  The `situational mechanism' \citep[][p 22]{hedstrom1998} is shown as arrow number 1, representing the way social conditions account for the way people might interact with one another.\footnote{It is interesting to note that Erwin Goffman did not seem to think that relational structures would have much affect on behaviour, and to the extent it did, he suggsts, it would be likely to result in a very simplified representation of that structure. He justifies his claims by arguing that face-to-face interactions are too demanding of the attention of participatns to allow for much preoccupation with external factors \citep{gibson2005}.} Clearly, the type of interactions people engage in depend on the context in which they find themselves. Romeo and Juliet would most probably not have had the chance to interact, if it were not for Capulet's masquerade ball, a context that allowed them to shed off certain parts of their identity (affiliations to rival families,) while at the same time liberating other parts (heightened hormone levels.) In the social sciences, one could investigate how the size of a community affects the way people interact, and more specifically in the field of social networks, the network of relationships is often taken as an exogenously given structure providing the backdrop and shaping who might interact with whom, and in what form.

\figuremacroWH{ImgColemanBasic}{Coleman's diagram: basic version}{Four types social mechanisms}{.6}

The second arrow is sometimes called `action formation mechanisms' and it represents the actual interactions at the micro-level. It consists of individuals engaging in social events, communicating, bargaining, exchanging ideas, struggling to reach an agreement, etc. These interactions might have certain results, yielding changes at the micro-level; people might decide to purchase a new product, change their political affiliation or quit smoking. More generally, this mechanism is associated with the way an individual's action might be shaped by prior interaction with others.  The set of actions at the micro-level might then  have (cumulative) consequences at the macro-level, either reinforcing or changing the properties of the system as a whole. For example, people's action at the micro-level could influence the group's identity. This link between the results of micro-level interactions and systemic outcomes at the macro-level, is   depicted in the diagram as arrow number 3. Links of this type could be one of two types \citep{abell2010}:\\


\begin{enumerate}
\item \textit{Definitional:} a macro-level attribute is defined by micro-level attributes and logically determined by them. For example, the size of the population is simply the number of individuals in it, the outcome of an election poll is determined by the ratio between the sums of the votes cast for each party in the ballots, the Global Domestic Product is simply the  sum of the outputs of every class of enterprise etc. As we shall in section~\ref{subsec:static} \citet{granovetter1973} proposes a definitional link between the strength of a tie and the transactions associated with it. This type of macro-micro link is sometimes referred to as \textit{supervenience} \citep{hedstroem2009}, \textit{constitutive}, \textit{analytical} or \textit{aggregation}. The difference between the micro-level properties and the macro-level is one of order, not one of kind. 



\item \textit{Contingent:} Macro-level attributes are linked to micro-level ones, but the relationship is not necessarily or logically determined. The term sometimes used is that the macro is something `over-and-above' the sum of micro-states, this difference between the `sum' and the macro illustrated by a time lag between the moment in which micro-states have reached a certain distribution and the moment that the macro has `caught on.' The slight slope of arrow number three, rising not only upwards but advancing slightly to the right as well, expresses this time lag, suggesting the macro needs to `catch up' with the micro and is therefore not logically defined by it, but has a trajectory of its own, empirically contingent on the micro but not logically defined by it. One could logically (or even empirically) conceive the same micro-state associated with different macro-states, so that the relation between the macro and the micro is not that of supervenience (see figure \ref{ImgDuckRabbitIllusion} for an illustration.) An example could be the price of a product, a macro-level feature that is an outcome of a processes of negotiation between sellers and buyers. In some types of transactions, such as the stock-prices, the price is calculated directly by an algorithm that depends on the aggregate number of buyers and sellers. In this case the micro-macro link becomes definitional and the Coleman diagram becomes practically squared (ignoring the time-lag it takes to calculate the stock price.) But when economists speak of price-stickiness, they refer to the process where some market participants have market power and are hence `price makers', while others are `price takers.' Demand might be low but for some exogenous reason a macro-result is obtained which is neither defined nor determined but contingent on the state of the various actors. This type of link is sometimes referred to as \textit{empirical}, \textit{synthetic} or \textit{causal}, and the difference between the micro-level property and the macro-level property is one of kind, not of order. 
\end{enumerate}


One way to adjudicate between the definitional and the contingent link is to ask oneself the following question: could there be a time-lag between changes at the micro-level of analysis and changes at the macro-level? Any such time-lag, no matter how small, is an indication of a contingent, not a definitional link between the micro and the macro. 

An example of how this theoretical framework could work in practice can be illustrated in the study of the dissemination of new pharmaceutical products \citep{coleman1957}. When studying the adoption of the product in a population of hospital doctors, the diffusion process was found to have a distinctive pattern. In the beginning, adoption was relatively slow, with the number of doctors adopting the product increasing at a modest rate. But with time, adoption rate accelerated and reached a maximum when roughly half of the doctor population have been won over. Adoption rate then slows down steadily until almost every doctor has adopted the new product. Depicted on a graph in which the x-axis reflects the progression of time and the y-axis reflects the number of doctors adopting the product, the process is expressed as a sigmoid (i.e., S-shaped) curve.

\begin{wrapfigure}{r}{0.40\textwidth}
  \vspace{-35pt}
  \begin{center}
    \includegraphics[width=0.39\textwidth]{ImgDuckRabbitIllusion}
  \end{center}
  \vspace{-20pt}
  \caption[Illustrating a contingent macro-micro link]{\textbf{Illustrating a contingent macro-micro link} - A single configuration at the micro-level (white and black pixels on the page) can be mapped into two macro-level meanings, a duck or a rabbit.}
  \vspace{-20pt}\label{ImgDuckRabbitIllusion}
\end{wrapfigure} 

The Coleman diagram suggests a way of analysing the process of diffusion. The population of doctors are connected to each other through an (exogenously given) network. Contingent on the contacts they have (arrow number 1) they begin to converse, exchanging their experiences and engaging in a debate about the new product, its advantages and disadvantages. The result of this interaction (arrow number 2) is a decision made at the level of the individual doctor, whether to adopt the new product or not. A simple aggregation yields the ratio of `converted' doctors (definitional link between the macro and the micro), a number that represents a `social outcome' at any given time, and the features of the graph represent the system as a whole. Mathematically, the differential equation expressing this interaction model looks like this:
\[ 
	\frac{dx}{dt} = \alpha x\left(N-x \right) 
\]
Where the rate of conversion $\frac{dx}{dt}$  depends on $x$, the number of those converted to the new product an $N$, the total number of individuals in the system. 

Surprisingly, the sigmoid pattern is only characteristic of hospital doctors, and not of those doctors working in their own practices. In the latter population, a different pattern arises, with a very rapid uptake up front, and the rate of adoption decreasing steadily with time and approaching zero when almost all of the doctors have adopted the new product. Graphically, an arc-shaped curve is obtained, not a sigmoid. Thus the characteristic structure of diffusion (which is a macro-level feature of the system as a whole) depends on the conditions of interaction for the population of doctors. This process is expressed mathematically like this: 
\[ 
	\frac{dx}{dt} = \beta \left(N-x \right) 
\]
According to Coleman's \citeyearpar{coleman1957} paper, the difference between the two populations of doctors is a result of the different ways in which their networks are structured. The structure of relationships in the hospital allows for more interaction between those doctors who have tried the drug and those who have not. Hospital doctors are embedded in a network that gives them access to information that is more reliable, namely the opinion of colleagues. The network structure of doctors working in their own practices is different in that their network of professional relationships is much more limited. Thus, it is not easy for them to get reliable information from disinterested parties such as colleagues in a hospital, forcing them to rely less on  the process of interaction and exchange and more on publicly available sources of information. 

\figuremacroWH{ImgColemanWithoutInteraction}{Coleman's diagram: with and without interactions}{Five types of social mechanisms}{.6}

\noindent The distinction between these two populations can be illustrated in the following elaboration of Coleman's diagram, shown in figure \ref{ImgColemanWithoutInteraction}. The decision whether to adopt a new technology is made at the level of the private doctor, but it could be driven by two mechanisms: one could involve a process of interaction and negotiation between doctors in a hospital setting (arrow number 2.) The second could involve features of the entire collective, such as publicly available information or simply the fact that the proportion of `converts' in the population has reached a certain threshold. Arrow $2a$ in the diagram reflects the possibility that choices are made independently of interaction and only contingent on certain properties of the system as a  whole \citep{abell2003}. 

Now, before turning to another elaboration of the basic Coleman diagram, a few words about the fourth mechanism, a direct link between one macro state and another that does not involve decision making and actions of individuals. It was \'Emile Durkheim who was accused of arguing for the possibility of mechanisms that operate `sui generis' at the macro-level. There is a certain appeal in entertaining this possibility, for it suggests a  symmetry between macro- and micro-level entities, implying that there is in fact no difference in kind between these entities. An interpretation of Durkheim's logic of macro-macro level mechanisms was presented by \citet{blau1972} in the context of a theory that links the effect of size (macro-level feature) on structural differentiation (also macro-level feature):  
\begin{quotes}
Another assumption is implied here: the prevailing characteristics of organizations, as distinguished from those in particular organizations, can be explained in terms of the influence of antecedent conditions in organizations (or their environment) without reference to the psychological preferences or decisions of individual managers, because these sociaI conditions greatly restrict the options of managers who pursue an interest in efficient operations. This principle derives from Durkheim (1938: 110): `The determining cause of a social fact should be sought among the social facts preceding it and not among the state of individual consciousness'
\end{quotes}

\noindent It is important to understand what is at stake here, and to question what meaning we would like to attribute to arrow number 4 type explanations. Following the logic of functionalism, Social actors do not play an important role when they make decisions that would lead to the optimal performance of the organization as a whole. I think it is not controversial that organizational changes occur as a result of decisions by individuals, managers or other parties, and that the ideas in the minds of these actors are part of the process that yield these changes. However, insofar as choices are made so as to optimize the macro-features of the organization as a whole, and assuming that only one option is the most effective, that is the decisions that actors are predetermined to make. The logic of functionalism is therefore coherent with mechanisms that operate at the macro-level, when an option is chosen because of its functionality with respect to its beneficial consequences at the level of the system as a whole. The properties of the individuals and the process of interaction at the micro-level is thus of no consequence, and the macro-conditions determine the macro-outcome, \textit{as if} they were independent of micro-social processes. I think that if we were to interpret arrow number four in this light, we would not need to reject the possibility that some social phenomena indeed proceed along this mechanism. 

Durkheim defended his view of social facts in his essay, `The division of labour in society' with the following words;
\begin{quotes}
The totality of beliefs and sentiments common to average citizens of the same society forms a determinate system which has its own life; one may call it the collective or common conscience. No doubt it has not a specific organ as a substratum, it is by definition diffuse in every reach of society. Nevertheless it has specific characteristics which make it a distinct reality. It is, \textbf{in effect,} independent of the particular conditions in which individuals are placed; they pass and it remains \citep[my emphasis, ][]{durkheim1997}
\end{quotes}

\noindent Notice the interjection `in effect.' Durkheim isn't proposing a process that is fundamentally detached from humans, but that \textit{in effect} and \textit{consequence,} proceeds \textit{as if} it were `independent'  of variations among individuals. It is hard to object to the notion that there exist certain constraints to which members of a group are all subjected, independent of possible variations between them. To the extent that variations exist, it is conceivable that these have no bearing on the macro-level. Understood in this way, I am not sure we need to reject, a-priory, the possibility of such macro-to-macro transitions. 

A last variant of the Coleman diagram that is used in this dissertation introduces a  meso-level of analysis into the picture (see figure \ref{ImgColemanWithMeso}). The idea here is to distinguish between the meso-level of tie formation and the micro-level of social actions. It is here that we first introduce the distinction into the Coleman diagram, differentiating between ties as durable structures connecting people, and the actual flows associated with these ties. I will attempt to use the Coleman diagram to assess how these two dimensions relate to one another, and what sort of explanations we need in order to bring them together into a unified theory of social networks.

\figuremacroWH{ImgColemanWithMeso}{Coleman's diagram: introducing the meso level}{Six different social mechanisms}{.6}

\subsection{Social (trans)actions}\label{sec:Chp2Transactions}
\noindent The links between social ties and the social actions with which they are associated, necessitate a short excursion into the nature of social action. The literature on this topic is vast \citep{danto1973}, and mostly irrelevant for the purposes of this investigation. However, I shall proceed by trying to identify the defining characteristics of a social action. Perhaps one of the first scholars to make the social action a pivot of social theory was Gabriel Tarde   \citep[quoted by][]{vargas2008}: 

\begin{quotes}
What is or rather what are social facts, the elementary social acts, and what is their distinctive character? [\ldots]  The elementary social fact is the communication or the modification of a state of consciousness by the action of one human being upon another. [\ldots] Not everything that members of a society do is sociological. [\ldots] To breathe, digest, blink one's eyes, move one's legs automatically, look absently at the scenery, or cry out inadvertently, there is nothing social about such acts. [\ldots] But to talk to someone, pray to an idol, weave a piece of clothing, cut down a tree, stab an enemy, sculpt a piece of stone, those are social acts, for it is only the social man who would act in this way; without the example of the other men he has voluntarily or involuntarily copied since the cradle, he would not act thus.  The common characteristic of social acts, indeed, is to be imitative. [\ldots] Here is, then, a character that is clear cut and what is more, objective. 
\end{quotes} \label{quote:Tarde} 

What defines something as an action for Gabriel Tarde, is the principle of imitation, which is closely related to the idea of diffusion discussed above. A different approach, and the one more popular today, is to define an action in terms of reason, intention and purpose. This idea was neatly elaborated by Marcel \citet[][p 21,59]{mauss1950}, in his famous study of the function and consequences of the action of gift-giving.
\begin{quotes}
Our festivals [in New Caledonia] are the movement of the hook that serves to bind together the various sections of the straw roofing so as to make one single roof, one single world  [\ldots] The gift is therefore at one and the same time what should be done, what should be received, and yet what is dangerous to take. This is because the thing that is given itself forges a bilateral, irrevocable bond. \\
\end{quotes}

Thus conceptualized, the act of giving a gift is not simply a disinterested act of generosity. It is a calculated transaction, an investment, a way of dealing with a possible turn of events in a risky and unknown future. There is a reason and a purpose to this transaction. It creates a form of social debt, and is therefore (possibly) bound with another future action, the action in which this debt will be paid off. These two defining properties of social action, \textit{purpose} and \textit{interdependence}, will be further elaborated in a moment, but before doing so let us note a second interesting point made in this quote, namely the link between the social transaction of giving a gift, and the tie that is being forged as a consequence. The transaction and the tie are not the same thing, and `tie formation' is not considered here a social act, in and of itself, but a consequence of the transaction(s), coupled by accepted norms of reciprocity.  

This second point, about the link between the meso-level of tie-formation and the micro-level of social transactions is further highlighted in the work of Georg \citet{simmel1908}. Consider the following qoute: 

\begin{quotes}
The large systems and super-individual organizations that customarily come to mind when we think of society, are nothing but immediate interactions that occur among men constantly, every minute, but that have become crystallized as permanent fields, as autonomous phenomena. As they crystallize, they attain their own existence and their own laws, and may even confront or oppose spontaneous interaction itself. \\ 
\end{quotes}\label{quote:Simmel} 

Again we have the separation between the `immediate interactions that occur \ldots constantly' and the crystallization of structure, possibly as a side effect of these interactions. Again we have a distinction between momentary events and that which has become rigid, reminiscent of Heraclitus' distinction between the flow of the river and the stable idea of a river. These here are two separate levels of analysis. 

Notice the difference between Mauss and both Simmel and Tarde, regarding the origin of action. Whereas Mauss thinks that gifts have one clear \textit{purpose} which is to `forge' the bond, neither Simmel nor Tarde speak of a purpose for action. Simmel's actions could have a completely different purpose. But the consequences, whether intended or not, are the same: the forging and crystallization of structure, organization, and laws. 

In contrast to Tarde and Mauss, Simmel does not speak of the defining properties of actions. However, on this issue Max Weber has an important insight: `We shall speak of `action' insofar as the acting individual attaches a subjective meaning to his behaviour \ldots an action is social insofar as its subjective meaning takes account of the behaviour of others and is thereby oriented in its course' \citep[p 4]{Weber1978}. At the very least, an action needs to have a `purpose' in order to be social. James Coleman, following Weber, claims that 'for some purposes in the theory of this book, nothing more than a common sense notion of purposive action is necessary' \citep[p 13]{coleman1990}. But that is not enough. For `purpose' to have any chance of being obtained, it must also be understood via common features shared by individuals, conventions and norms (at the macro-level) that allow for others to interpret the meaning of actions, the intention and purpose motivating them, and the expectations for an adequate response on their part.

To illustrate what Weber and Coleman have in mind, consider the following distinction between a social action and other forms of non-social behaviour, the distinction between a wink and a blink (or some other involuntary twitch of the eye;) `two boys fairly swiftly contract the eyelids of their right eyes. In the first boy this is only an involuntary twitch; but the other is winking conspiratorially to an accomplice. At the lowest or thinnest level of description the two contractions of the eyelids may be exactly alike. From a cinematographic film of the two faces there might be no telling which contraction, if either, was a wink, or which, if either, were a mere twitch. Yet there remains the immense but non photographable difference between a twitch and a wink.' \citep[][p 480]{Ryle1971}.

The nature of these `immense' differences was articulated by Michael  \citet[p 15]{oakeshott1991}, stating that a wink `is an exhibition of intelligence, a subscription to a \textit{practice} and [motivated by] \textit{reason},' whereas a blink, he says,  `is a component of a \textit{process} to be understood in terms of a \textit{law} or a \textit{cause}'.\footnote{I can imagine some counter arguments about the validity of these distinctions. Just like a wink, a blink might also be said to be functional. It is used to spread moisture and remove irritants from the surface of the cornea, and is therefore also oriented to the future similar to the way that a wink is oriented to future transactions. The distinction between reason and cause is one wrought with controversy, but for our purposes not entirely relevant.} 

\figuremacroWH{ImgTransactionInterdependencyMeaning}{Defining features of social transactions}{consisting of \textbf{\textit{Interdependency}} and Meaning (or \textbf{\textit{Purpose}})}{.8} 

The  defining properties of social action are therefore twofold (see figure \ref{ImgTransactionInterdependencyMeaning}.) First, what I would call \textbf{\textit{interdependency}}, here understood on two levels; in terms of the association between people  \cite[`To act is always to act \textit{with} others'][p 54,]{ricoeur1984} and in terms of the associations between one transaction and another, either within stimulus-response type of exchanges, or in the way every transactions is a token belonging to a type of transactions, in Oakeshott's formulation a `subscription to a practice,' and in Tarde's formulation an imitation of other token actions (a nominalist like Tarde rejects the notion of abstract types.) So for example, a token wink is associated with all winks experienced in the past, and those ascribe it with meaning.

Ascribing `meaning' to a transaction is the reason for interdependency between transactions. Each and every transaction in a chain is given meaning through the chain it constitutes, just as every word in a sentence is given meaning by the sentence it constitutes, for actions cannot be 'understood or explained unless they are related to the actions of others' \citep[p 35]{Hedstroem2005}. In addition, the meaning of a token transaction is carried from the category of human practices to which it belongs, a category whose meaning is assumed to be shared between people.  

The `meaning' of transaction is associated with its second defining property which I will refer to as \textit{\textbf{purpose}}, closely related to the notions of reason and intention. Transactions are initiated for a reason, as opposed to the  automatic effect of a cause. Something has a reason if it is oriented to an event in the future, whereas something with a cause is oriented to an event in the past. 

The fundamental principle in micro-foundation analysis is that social change needs to be analysed in terms of individual transactions. Sociologists adhering to this doctrine include much of the classical German tradition (Weber and Simmel), the classical Italian tradition (Pareto and Mosca) and sections of American sociology (Parsons, Merton and Coleman.) We find related modes of thinking in economics, of which both the classical and the neo-classical variants share the principle economic phenomena can be analysed in terms of an accumulation of elementary individual actions \citep{boudon1986}. 



%In turn,  And that interaction constitutes the “specificum sociologicum,” in von Wiese’s words (Franzosi 2004a,b, pp. 260–262)


It is no surprise that social scientists continue today in the pursuit of this paradigm, especially in regards to the study of social change. There is no reason why the paradigm should be confined to economics, as Max Weber has noted, where it had been widely accepted since Adam Smith's time. It has a universal nature, and according to \citet{boudon1986} it is `probably one of the most important discoveries in the modern social sciences (though not always recognized as such).' 

% \input{2/chapter_2_sub_1}

\section{Social Networks in light of the Coleman diagram}\label{sec:NetworksInLight}
\begin{quotes}We concentrate on the structural properties of elementary social relations as a first step towards understanding how structure in social relations arises and evolves [\ldots] For our purposes, relations are taken as givens. \citep{Holland1977}
\end{quotes}  


\begin{quotes}`\ldots the underlying process for network change is assumed to be located in the network structure' and in the evolving `characteristics of network members' \citep{Doreian2002}.
\end{quotes}  

\noindent Perhaps Durkheim would embrace the ideas expressed in the quotes above, but I wouldn't be surprised if Tarde, Mauss, Simmel and Weber would be taken aback. According to the network scholars quoted above, the whole project of social action, the entire effort associated with establishing, consolidating and maintaining alliances between partners is rendered all but irrelevant for the evolution of the network.  

There are two possible counter-arguments, the Durkheimians would probably say that such micro-level phenomena are nothing but `airy chaff, posing little resistance to network effects which, given enough time, will carry the day' \citep{gibson2005}. I argued above that such a Durkheimian approach needn't be rejected at the outset, especially when  the entities in question follow a long term, consistent functionalist agenda, hell-bent on forming ties or dissolving them, opportunistically taking advantage of situations in order to pursue their goals. But this kind of explanation is limited if we wish to account for ties that form as a consequence of unintended, long term interactions, the kind Simmel described in the quote above and Ibn-Hazm warned of in the poem that opens Chapter 1. 

Another reply could be that something akin to action, \textbf{\textit{is}} in fact taken into account. For example, the formation of ties and their dissolution, as well as changing `characteristics of network members'\citep{Doreian2002} are rather like social action, in the sense that they are more or less situated in time and place, involving more than one person, all the features of a micro-level phenomenon. But upon second thought it would be peculiar to argue that the formation of a new social tie falls under the same category of the act of winking at someone, for example, or making a speech utterance, etc. In contrast to a social action, forming a tie requires the alignment of interests and purposes of two people, not just one. Besides, every social tie could be associated with multiple social actions, including acts of communication, interaction, exchanging of gifts etc. Finally, we still have the problem of accounting for ties that are formed as a side effect of other intentions, the consequence of a path-dependent process. 

To explore these ideas further, the rest of this chapter organizes a sample of network studies with respect to their relation to the Coleman diagram as depicted in figure \ref{ImgColemanWithMeso}. Three types of work are considered:  1) some studies focus on static networks without giving much attention to events or change. However, parts of this work do establish important connections between different levels of analysis, 2) others study macro-meso links, consisting of tie formation and dissolution, and how these are related to the network topology, and  3) The third body of work study macro-meso-micro processes operate  within all three different levels of networks, ties and sequences of related social transactions, constrained and facilitated by an evolving network structure. 



\subsection{Static Networks}\label{subsec:static}
The first body of work studies static properties of networks, often with an eye to  features that distinguish social networks from other types of networks \citep{newman2003a}. Probably the most quoted \citep{lazer2009a} example of an unintuitive finding from this body of work is the `strength of weak ties' hypothesis \citep{granovetter1973}, a hypothesis first tested on a large dataset almost 35 years after it was published \citep{onnela2007}. The `strength' of a tie is defined by `the combination of amount of time, emotional intensity, intimacy and reciprocal services characterizing a tie' \citep{granovetter1973}. 

This definition, in and of itself, is an example of a link between the meso level property of the tie and the micro-level of transactions. The strength of the tie, which is a meso-level property, is defined in terms of the frequency and rate of transactions, the cumulation of time and emotional intensity people associate with them as well as the likelihood of observing reciprocation. The relation between meso- and micro- is a definitional one. However, this is more than a definition - it is an empirical statement about the link between, for example, frequency of interaction and the likelihood of reciprocity. Empirical studies haven't always been successful in verifying this link \citep{kovanen2010}.

According to the hypothesis, strongly tied pairs typically share more friends in common than weakly tied ones. Thus, people's weak ties lead them away from their ordinary social circles into more distant parts of the network, making those ties crucial for the global connectivity of the network, but also for gaining access to new information. To take this logic to an extreme, people who haven't spoken with one another for a long time have much news to exchange, because their connection is a form of a bottleneck between distant communities, the only one by which this news can travel. In contrast, when calling a close friend, one shouldn't expect to hear news they could not have obtained from other sources. 

\figuremacroW{ImgSwot}{Testing the Strength of Weak Ties Hypothesis}{Nodes within clusters are connected by `strong' ties whereas clusters are connected by `weak ties.' The strength of the tie represented in the figure by color and measured by proxy as the aggregate duration of phone calls between every two nodes  \citep{onnela2007}}{.6}

Although this body of work does not dwell explicitly on processes of change, it does establish interesting links between different levels of analysis. There is an important link between the meso-level of tie strength and the macro-level of the topology of the region in which the tie is embedded. Strong ties are embedded in tightly knit regions and weak ties act as bridges. Tell me the level of clustering  of the region in which a tie is embedded and I shall tell you the strength of the tie (or the other way around.) 

Another link exists between the meso- and micro-levels of analysis: first, weak ties (meso-level tie attributes) are the sites in which new information flows (micro-level transactions.) Of course, this micro-meso link has consequences at the macro-level: since bridges are activated relatively infrequently, the social network is poorly designed for the quick dissemination of new information at a global scale. Granted that global social networks do in fact exhibit properties of a small world in the sense that, ultimately, everyone is connected to most everyone else through a surprisingly small number of degrees of separation. However, since the most important ties for connectivity are activated so rarely, in practice diffusion on a global scale is hindered - not only by the structure of the network, but also by the `burstiness' of activity \citep{karsai2011}. 

A functionalist approach would immediately raise the following question: if they are not `designed' for the dissemination of new information, why are they structured this way? Investigations of the static properties of social networks suggest that humans tend to departmentalize into clusters, each cluster `circling its wagons,' a structure that might be explained by the need to build and maintain the social capital of communities \citep{karsai2011,coleman1988,onnela2007}.  

I would like to introduce another network example to show how features at the macro-level of analysis could directly impinge on individuals, leading them to make social choices without the process of interaction or conscious deliberation, as in arrow $2a$ in figure~\ref{ImgColemanWithoutInteraction}. It is as if macro-properties operate `behind the backs' \citep{hedstroem2009} of the actors, without them being fully aware of the reasons (or rather causes?) that have led them to choose as they have. I am referring to a study \citep{Bearman2004} of sexual networks of adolescents in a high school of roughly a thousand students in the Midwestern United States (see figure~\ref{ImgSexualNetworks}). The network has a few properties that are uncommon to other forms of networks. First, it is not a small-world network, having neither the random ties that create short average paths, nor the high level of clustering that is so common to other types of social networks. Triangles, which are all but ubiquitous in friendship networks, are found here only once (close to the upper right corner of the diagram.) The reason being is that a triangle would necessitate at least one sexual relationship between two persons of the same sex, and the study was made on a population which was (reportedly) mostly heterosexual. 

\figuremacroW{ImgSexualNetworks}{Romantic network of adolescents in an American high-school}{the structure of sexual relationships observed over a period of eighteen months, every node representing an individual, ties represent sexual/romantic relationships. Taken from \citet*{Bearman2004}}{0.7}

Besides triangles, the next order of closed cycles (and the minimal one possible in a heterosexual population) is cycles of order four, representing a situations of pairs switching partners, say from ( $\left\langle \text{Male}_1, \text{Female}_1\right\rangle , \left\langle \text{Male}_2, \text{Female}_2\right\rangle$ ) to  ($\left\langle \text{Male}_1, \text{Female}_2\right\rangle , \left\langle \text{Male}_2, \text{Female}_1\right\rangle$ ). Such a switch would constitute a cycle of length four. From the point of view of one of the males, he has formed a partnership with his ex-girlfriend's current boyfriend's ex-girlfriend. However, we find no such cycles of order four in the network, and there appears to be a norm that makes people avoid such pair swapping excercise. This avoidance most probably springs from an analog to an incest taboo \citep{Moody2009}, since a relationship that would close a four-cycle appears too intimate. Dynamically this is an interesting type mechanism since the prohibition law develops over time, a partner that would be acceptable at time $t_1$ is prohibited in time $t_2$. The prohibition is localized in place and time, but it has an effect on the macro-properties of the network, increasing the length of cycles, making it different from `small world' networks and hence prolonging the time for sexually transmitted diseases to diffuse throughout the community. 

Thus, the first body of work treats the network as a relatively static structure, one that does not change much over time. Any micro-transaction that takes place in the network is assumed to unfold in an exogenously given structure, pre-determined and relatively unchanging. 


\subsection{Macro-Meso links}\label{sec:Chp2MacroMeso}

But social networks do evolve, people who were once strangers or distant acquaintances become friends, and close friends drift away. Thus, the second body of work studies the evolution of networks themselves, the mechanisms that govern the likelihood of changes at the level of ties, meso-level events that may have consequences at the macro-level of the network. These so reffered to as `network events' are of two types; first, the `event' by which properties of individuals change when they acquire new behaviour patterns, changing their smoking, eating or drinking habits, altering their political affiliations etc. These changes are understood to be influenced by people's position in the network, and are therefore known as \textit{influence} models \citep{Friedkin1999,robins2001a}. In contrast to influence, \textit{selection} models consist of mechanisms to explain how people select their friends, a dynamic consisting of changes in the status or the properties of the relationship between two individuals. People can form new ties, disband an old ties \citep{robins2001} or else change the affect attached to existing ties, say from positive feelings about someone to negative ones \citep{Doreian2002}. Notice that the literature does not refer to these as `actions,' but as network events. 

Clearly, people's personal networks change most extensively when they change their life's circumstances, when they move between jobs or relocate for example. Such changes provide an opportunity to study in detail the process of tie formation and dissolution. It also provides an opportunity to compare between one's personal network in different contexts. Since the same person establishes relationships in different settings (different conditions for individual action, arrow number 1 in the Coleman diagram,) we might expect certain things to change and others to remain the same. One thing that remains the same, at least at first, are the properties of the person who moved. Specifically, consider the `social brain' hypothesis \citep{dunbar1998,dunbar2007}, the theory that states that people's brains are wired with stable cognitive properties that influence the structure of their personal network. These properties are unique to individuals, and may differ from one to the other in terms of an individual's preferred size of their personal network for example, or in terms of the way individuals prefer to allocate time to their different friends. 

The social brain hypothesis suggests that geographical relocation would have an effect on personal networks in the sense that the identity of their contacts might change while maintaining something of the structure of the personal network. This hypothesis has been actually confirmed in a rather interesting empirical study \citep{saramaki2012} of 30 students who just completed school and moved away from home to attend a university elsewhere.

A considerable variance between individuals was identified, in terms of the distribution of time each allocated to their alters; some prefer to have just one or two best friends and allocate most of their time to them, and hardly any time to anybody else. Others allocate time more evenly between numerous acquaintances. After the relocation, the composition of the personal networks changed substantially, with many new people entering and old ones leaving it. However, each individual maintained the way they distribute their time among their friends. Thus, each individual seems to carry a `social signature' in the way they distribute time among their alters, signatures that vary remarkably between individuals. And though life circumstances may change the identities of those they interact with, these signatures stay surprisingly persistent. 

The structure of the network at the macro-level is therefore contingent on the possibility of matching between different types of structure of cognitive fingerprints. Relocation of a group of people into a new context is like a shock to the system at the macro-level, the upper left corner of the Coleman diagram. There follows a negotiation between people, and the process of friendships formation is constrained by the cognitive structure that each individual brings into the new context, resulting in a final network in which the constraints of each of the individuals is fulfilled, more or less. 

Relocation is an exogenous event that prompts all three types of network events: tie formation, dissolution and changes in one's character. But there are other types of mechanisms that are responsible for such events, three of the most well studied ones consist of the popularity effect, homophily and triadic effects.\g

In all three types of mechanisms, an existing network structure is exogenously given at the upper right hand corner of the Coleman diagram, consisting of individuals, their properties and the ties that connect them. The different mechanisms mobilize the occurrence of events across the network, at times working in the same direction to strengthen certain topological properties, at times working in opposite directions \citep{wimmer2010}. These local changes then have cumulative effects at the macro-level of the network. Thus the upper part of figure~\ref{ImgColemanWithMeso} unfolds, linking meso-level network events with the evolving macro-structures. 
 

\subsection{Macro-Meso-Micro links}

The preceding section covered mechanisms labeled 1', 2' and 3' in Coleman's diagram~\ref{ImgColemanWithMeso}. What remains is to complement the picture with the bottom part of the diagram. The question here is how to capture both levels at once - the (possibly changing) topology of the social network and the sequences of related social transactions. 

Consider what we can learn by focusing on the exact moments in which people initiate telephone calls. These reveal sudden bursts \citep{barabasi2005} of activity: patterns that are neither completely regular nor random, but are characterized by long periods of silence followed by quick succession of calls, very inhomogeneous, uneven distributions that appear to be intrinsic to the way humans communicate. But research that falls into this category needs to take into account the defining properties of social transactions and particularly the links between the messages themselves. For example, receiving a message from someone should be seen as a stimulus that requires a response, either by way of replying to that message, or by forwarding it on to a third person, or by any other type of social transaction one might want to think of. This interdependency between messages becomes lost if we simply aggregate all transactions or study their distribution in time.

Before showing examples of research that accounts for social transactions, let us turn an eye to the way social network scholars have approached this issue. 

\subsubsection*{The Durkheimian Strategy: Ignoring Transactions}\label{sec:Chp2Durkheimian}




The first strategy was already introduced in the quotes opening section~\ref{sec:NetworksInLight} \citep{Holland1977,Doreian2002}. The subject matter of social networks is presented as the social, durable structure, an entity that follows its own laws independently of micro-social interactions. This was the favoured strategy, quite explicitly stated by the founding fathers of the field of `social networks.'


\begin{wrapfigure}{r}{0.25\textwidth}
  \vspace{-10pt}
  \begin{centering}
    \includegraphics[width=0.24\textwidth]{ImgHumpingBarnes}
  \end{centering}
  \vspace{-20pt}
  \caption[Portrait of John Barnes]{\textbf{Portrait of John Barnes} The front cover of his \href{http://www.lulu.com/product/paperback/humping-my-drum/2791628} { autobiography} \citet{barnes2008}}
  \vspace{-10pt}
\end{wrapfigure} 

It is widely accepted \citep{mitchell1969, caulkins1981} that the first scholar to have explicitly used the term `networks' to denote a social field was John Barnes. An anthropologist who recently passed away, Barnes was also the first keynote speaker at the 1982 Sunbelt International Social Network Analysis Conference. But he is not only credited with coining the expression `social networks' and using it systematically in social science research, he is also acknowledged \citep{mitchell1969} as the first to point out the features that distinguish social networks from other social units of organization such as `class' or `group.' 



\citet{barnes1954} also makes a clear distinction between networks and interactions. He writes, and \citet{mitchell1969} quotes him on this, that the `social network' is a concept applied to `what is left behind when we leave out groupings and {\itshape chains of interaction}' (my emphasis.) The reason he gives for leaving interaction out of networks boils down to their ephemeral nature: 'These units', he says 'do not necessarily persist through time, nor does their membership remain fixed' \citep{barnes1954}. Therefore they do not qualify to be relevant to the network. One can almost hear the voice of Durkheim echoing through these words, claiming that the macro evolves \textit{in effect} independently of variations at the level of individuals. 


Mitchell agrees with Barnes that the concept of social networks should be kept analytically separate  from the concept of social interactions. He develops this idea further and discusses a controversy in the literature regarding the question of how we should understand the `content' of a social tie, while dismissing arguments advanced by other scholars who insist on the relevance of the `flow of information' for the study of social networks. Instead, he suggests that the study of networks should be limited to `the normative context in which interactions takes place,' this `normative context' consisting of interpersonal expectations that regulate transactions and their permissible interpretation. 


\subsubsection*{Definitional Strategy: Ties defined by multiple transactions}\label{sec:chp2Aggregation}
Consider how the following definition of communication networks compares to the ideas expressed above:
\begin{quotes}
`Communication networks are the patterns of contact that are created by the flow of messages among communicators through time and space [a message refers] to data, information, knowledge, images, symbols and any other symbolic forms that can move from one point in a network to another or can be co-created by network members'  \citep*{monge2003}
\end{quotes}
 
\noindent Ostensibly, it is precisely what Barnes and Mitchell hoped to leave outside of social fields of networks, that \citet{monge2003} bring  right back in. Moreover, they seem to adopt the opposite extreme to Durkheim, the idea that there is nothing \textit{\textbf{but}} transactions, and that social networks are \textit{\textbf{defined}} by the aggregate of all transactions observed within a specified time-window.\footnote{But perhaps this is a misinterpretation: the authors say that `patterns of contact' are `created.' What is unclear is how are these patterns created and what are the consequences of this creation? Are they simply created in the minds of the scientist observing and looking for them in the data? Or are these patterns created also in the minds of the actors in the network and affecting their actions? Unfortunately, \citet{monge2003} do not explore these questions.} 

This strategy of defining ties, neither as `structure' nor as a `normative context,' but as flow alone, resonates with the definitional conceptualization of the link between the macro and the micro, as described in section~\ref{sec:colemansboat}. The macro thus defined supervenes on the micro, with no change in any of the macro-features logically conceivable without a change on the micro-level. This  approach is shared by different scholars throughout the decades. Consider for example the claim made by the great George Caspar Homans in relation to groups \citep[p 84]{homans1951}: `a group is defined by the interactions of its members.' \label{quote:Homans} Only interactions and nothing `over and above' interactions. And if we take the tie to be nothing other than a group of two, we see that Homan's definition of the group collapses into something similar to what \citet{monge2003} have in mind. Max Weber also seems to belong to the group, when he says that `the social relationship \ldots thus consists entirely and exclusively in the existence of a probability that there will be a meaningful course of social action' \cite[p 26]{Weber1978}.\footnote{Whether `probability' of transactions and their aggregation amount to the same thing is an open question, but I suppose that they are very much closely related.}

%However, there are two challenges to this argument, one theoretical and one methodological. The theoretical challenge is that the use of communication data as an indication for underlying social relationship invites the view that social relationships are equivalent to (the aggregate of) social transactions. This is sometimes referred to as 'the constitutive' view \citep{abell2010}, where the macro-social entities are seen to be constituted, or defined by a simple aggregation of the micro-entities. This view could be useful for simplification purposes, but once transactions between actors are aggregated, it is no longer possible to develop a mechanism based explanation that operates across the micro-macro levels of transactions and relationships. Furthermore, the process of transforming the transaction-data-set into a set of nodes and ties whitewashes precisely what made the transactions `social' in the first place, namely the fact that actions cannot be 'understood or explained unless they are related to the actions of others' \citep[p 35]{Hedstroem2005}. 


This approach raises two concerns, one theoretical and the other  methodological. If network ties are nothing but the aggregate of the flow of transactions, what meaning should we ascribe to this network? What do these ties represent in the real world? 

One answer could be that transactions are treated as an \textit{indication} of underlying social relationships. The object of research is therefore not the transactions per-se, nor their aggregation, but latent, more meaningful social ties, becoming manifest only indirectly through observable transactions. Indeed, it seems reasonable to assume that when people interact frequently, they may know each other and may be related to each other in a meaningful social bond. This argument rejects the notion that social ties are defined by social transactions, and the relationship between the micro and the meso becomes not definitional but contingent (see section ~\ref{sec:colemansboat} and the related discussion in section~\ref{sec:Chp6DeNooy}.)

But recall that transactions were defined in terms of their interrelatedness, each transaction a link in a chain of related transactions. The process of transforming the transaction data-set into a set of nodes and ties whitewashes precisely what made the transactions `social' in the first place, emptying them from their purpose and `meaning' in the Weberian sense of the word. If we simply aggregate the transactions into streams of messages without attention to sequences of social action, it is not clear that we arrive at `rock-bottom explanations,'\footnote{The idea that micro-foundations should reach `rock-bottom' explanations that involve individuals and their social action was advanced by \citet{watkins1957}} which is what the doctrine of micro-foundations requires.


A related problem on a methodological level will be elaborated in the next chapter, but in essence it is this: there are numerous ways to transform data streams of transactions into network models. This is because network models consist of ties representing dyadic relationships, whereas the data consist of sequences of related transactions that transcend the level of the dyad. Collapsing the rich properties of transactions into network models requires the modeller to make numerous ad-hoc decisions, and there is no standard against which one could validate whether one process of building models is superior to another. 

\subsubsection*{Third Strategy: Taking Transactions Seriously}\label{sec:chp2TakingTransactionsSeriosly}

How can we study the topology of social networks while taking not only individuals and ties, but also the transactions between them? I shall begin by making a controversial argument for the difference \textit{in kind} between social ties and social transactions, and then briefly review some studies that look not (only) at the aggregate of transactions but about their interrelatedness. 

It was Georg Simmel in the quote above (see page~\pageref{quote:Simmel})  who contrasts most clearly between social transactions and ties, when he speaks of `super individual systems' (such as ties), developing their own laws, and even `confronting and opposing interaction itself.' It is surprising to consider that a tie may serve not to facilitate the flow of transactions but, quite the contrary, in order to stop them from happening. But this would be a strong argument against the claim that ties are nothing but the aggregation of transactions. Simmel's claim can be empirically illustrated in an impressive study  of low-income African Americans from a mid-western city in the United States \citep{Smith2005}, an investigation of the causes for low-employment rates in these communities. Previous studies have challenged a widely held assumption, that continued unemployment is partly due to the community's isolation from sources of information and influence among those employed. Members of the community were found to be well connected with employed individuals, friends and relations who could provide timely information regarding job opportunities in their own workplaces. They \textit{could} provide that information, but chose not to do so. 

Those employed did not act to improve the employment situation within their network; they were often reluctant to wield their influence or even to provide information about job opportunities. The reason for this was that they were concerned that job seekers in their networks might act `too irresponsibly on the job, thereby jeopardizing contacts' own reputation in the eyes of their employers'. \citet{Smith2005} concludes that one primary reason for sustained unemployment in the community is not the lack of potentially useful relationships, but the failure to mobilize these relationships and to realize the social capital for unemployed individuals. 

And so we arrive full circle back to Simmel's claim, since it was concern for the integrity of ties between employed and employer, that throttles information flow between the employed and their unemployed friends and relatives. 

This case provides motivation for a distinction \textit{in kind} between the existence of social ties and the transaction between people. `[R]elationships have ontological status even when they are not being directly acted upon. Two people, for instance, can be considered `friends' even when they are not interacting' \citep{gibson2005}. The contrary may also hold true, when social interaction takes place without involving a meaningful social bond. The separateness of the two concepts is neatly expressed in the title of \citet{adams2010} letter to the Proceedings of the National Academy of Sciences (PNAS): `Distant friends, close strangers.' Here the words `close' and `distant' refer to physical proximity, the four-word-title suggesting that face-to-face interactions, just like other forms of human contact, is analytically separate both from the notion of social relationships, and from the normative commitment and social bond this notion entails. 

Finally, recall the three popular mechanisms operating at the meso-level of the tie, namely popularity effects, homophily and triadic closure \citep{snijders2006}. Despite the frequent referral to them in the social networks literature, many are still worried with the `inadequacy' \citep{snijders2006,newman2003} of these mechanisms, partly because they are still not well understood in terms of the micro-social processes that give rise to, and sustain them. It is infrequent that people `decide' to establish new relationships or dissolve old ones, since changes in the status of ties are themselves the result of a culmination of events involving various opportunities, choices, emotions, circumstances and mutual social transactions \citep{Lazarsfeld1954,hartup1997}. The literature on friendship \citep{hartup1997} makes   an important distinction between deep-structure (based on reciprocated emotions or perceptions)  and surface structure (social exchange), and exploring the interaction between these two levels implies that they are not only interdependent, but that each enjoys some level of (ontological) autonomy. 


How would one go about exploring social networks and the underlying sequences of social transactions? One way to go about it is to investigate those sequences of transactions in and of themselves, such that $A$ calls $B$, prompting a call from  $B$ to $C$, prompting the latter to return the call etc. One such study by \citet{kovanen2013} followed sequences of related transactions, investigating how these depended on attributes of actors engaging in them. For example, transaction chains consisting of men were found to be invariably shorter and less complex than those consisting of women. 

Another group of studies \citep{butts2008, brandes2009, denooy2011} seeks to predict how sequences are likely to unfold given a data-set of transactions. These studies model the expected waiting times between successive transactions, and the identities of actors who may initiate future transactions. Though the models predict temporal dependencies between transactions, they, too, do not consider the links of meaning between them. That is to say, when transactions follow one other in succession, we do not know whether one has prompted the next. Analytically, the objective of these studies is to develop new statistical methods for the analysis of transaction data-sets. 

Common to this type of work is the focus on transactions as events, just like network events. To the extent that there is reference to a distinction between ties and transactions, this is  taken to be one of order, not one of kind \citep[this is made explicit in a paper by][p 191-192]{butts2008}. Consequently, there is no attention to the study of co-evolution processes that operate between different levels of analysis. 


A second line of inquiry takes the network of relationships as exogenously given and follows the way transactions unfold within this network. Diffusion studies would arguably fall into this category, depending on how we might understand the term diffusion. Many such studies, specifically those that explore the spreading of disease, follow the way a certain property of a focal actor's friends affect changes in properties of the focal actor. But I am not sure we would want to say that changes of an actor's properties should be considered a `social action.' Gabriel Tarde would disagree to some extent, recall from the quote above (page~\pageref{quote:Tarde}) that a transaction is `\ldots the modification of a state of consciousness by the action of one human being upon another.' And though infection by a virus might modify one's state of consciousness, I do not think that this is what Tarde has in mind when he speaks of a social transaction. What is lacking from the infection is the second defining property of social action, and that is the notion of purpose and reason. 

Another kind of research that might fall into this line of inquiry belongs to a branch of social psychology known as the study of expectation states. These studies are based on the premise that social actions are shaped, facilitated and constrained by cognitive states with distinctive `structures' \citep{Balkwell1991}. For example, the rate and nature of utterances  in conversations have been shown to be shaped by properties of social relationships such as authority and deference \citep{Shelly2001, Johnson1994}, or the degree of familiarity and intimacy \citep{Boxer1993}. In a particularly interesting study, David \citet{gibson2005} devised a classification for turn-taking in a conversation (which he calls participation-shifts.) He traced the discussions of ten groups of managers who frequently work together and concludes that the pattern of their turn-taking is contingent on their relative positions in a network of friends, co-workers, and reporting relationships. 



Although findings seem to vary from paper to paper, the study of interactions provides strong evidence that the process of social exchange hinges on `the structure of the interaction'  \citep{Hedstroem2005}. In other words, exogenously given social ties govern practices of communication and interaction, the mechanism represented by arrow number 2 in the Coleman diagram (figure~\ref{ImgColemanBasic}.) 



  
  
The other direction of influence from transactions to ties (arow number 3) has been studied to some extent in the context of the formation of dominance hierarchies  \citep{Fararo1994, Skvoretz1996}. These studies formulate and test the mechanisms by which dominance relationships are shaped by a succession of dyadic encounters between animals. However, some scholars are concerned that these studies follow a `stylized account of interaction', and do not incorporate `insights into conversational rules' that regulate the transactions of human societies \citep{gibson2005}.
 
 
  \begin{wrapfigure}{r}{0.21\textwidth}
     \vspace{-40pt}
     \begin{center}
       \includegraphics[width=0.20\textwidth]{ImgChainLetter}
     \end{center}
     \vspace{-30pt}
     \caption[Networks of chain letters]{\textbf{Chain letters produce unusual network structures} - not small world networks but trees \citep{liben2008}}
     \vspace{-10pt}\label{ImgChainLetter}
   \end{wrapfigure}
 
One rather remarkable exception is a paper \citep{liben2008} that investigates the formation of diffusion networks from a detailed study of micro-social transactions. The authors trace a process by which  massively circulated Internet chain letters spread on a person-by-person basis. To their suprise they discover that the network representing the flow of chain letters is very different from the `small-world' network one would expect. Instead, the network progresses in a narrow but very deep tree-like pattern, continuing for hundreds(!) of steps, as depicted in figure \ref{ImgChainLetter}. In one of these networks, the median distance to the root over all nodes was nearly $300$, and more than $90\% $ of the nodes had exactly one child. 



Assuming that the signatories of the chain-letter were connected in a typical `small-world' network, how did this diffusion structure come about? Why doesn't it resemble the structure of the social network from which it springs? What could have possibly been the series of actions taken by the email users, so as to produce this unusual structure? Even after modelling a network in which only a fraction of the recipients forwarded the chain letter to their friends, this tree type structure could not have been obtained. 


The researchers then added a few extensions to the basic model of diffusion, emulating the way people use the technology of emails. First, they modelled the asyncronous nature of emails, having each recipient wait a length of time before acting on the message, a time distributed according to a power function. Second, they introduced three types of responses on the part of recipients: the recipients could either discard the incoming mail, they could forward it to their contacts or they could hit `reply-all' and group-reply to the set of corecipients on the original email message they received. 

These two extensions had a  `serializing' effect in networks with tightly knit regions. That is because if two recipients of an incoming email are mutually connected, the first to act on it may forward it to the other, producing a single long list with names rather than many distinct shorter lists, each containing one name. The interaction with the technology produces deeper `runs' of nodes in which each node has exactly one child, precisely the structure that observed. This study takes all the ingredients of the Coleman diagram in figure \ref{ImgColemanBasic}. It takes the small-world network as exogenously given, adds the micro-social rules of interaction that depend on the specific technology of emails, and yields a diffusion structure of a very different kind than the one that originated it. 

\section{Summary and Reflections}
This chapter introduced some of the key theoretical concepts in the literature of micro-foundations, focusing on the Coleman diagram and the way it organizes different types of social explanations. Two types of macro-micro links were discussed, the definitional and the contingent link. The theory was then applied in the context of social networks. Three types of network studies were identified. 
\begin{enumerate}
\item \textit{\textbf{static networks}} The first type of work focuses on static social networks searching for interesting patterns in the data. Already here we identify micro-macro links, for example the link between the strength of a tie (property the meso-level) and the topology of the region in which it is embedded (property at the macro-level.) 
\item \textit{\textbf{macro-meso}} The second group of studies investigate network dynamics, but limit themselves to three or four `network events,' consisting of tie formation, tie dissolution and the changing properties of ties and individuals. This type of work includes virtually all the empirical work based on longitudinal panel waves of traditional network datasets.
\item \textit{\textbf{macro-meso-micro}} The third body of work recognizes and acknowledges the existence of underlying social transactions. Within this body of work we see three strategies to deal with transactions. The Durkheimian strategy acknowledges transactions but maintains they are irrelevant for networks. This strategy was supported and argued for by the founding fathers of network analysis. The second strategy defines ties in terms of transactions (the link between the micro and meso is \textit{definitional}.) The third strategy is to take transactions seriously and study interdependencies among them. 
\end{enumerate}

\noindent The network literature that links the micro and the macro is vast, but there are only diffuse attempts to articulate precisely how the structure of social ties give rise to patterns of interrelated communication transactions, and how those in turn shape network structures (co-evolution mechanisms.) A full-fledged and systematic synthesis of the `interaction order' \citep{Goffman1983} and what we may call the `network order' is difficult to come by. One reason is perhaps the difficulty in gaining access to independent data on transactions and social-tie data \cite[for an exception see][]{quintane2011}. Two such sources of data would allow for a direct test of the hypotheses involving both levels (although this is not necessary for studying such micro-macro link, as will be argued in Chapter 6.)  

Another reason suggested by  \citet{gibson2008} is based on institutional inertia, driving a wedge between the perspectives of `interactionists' and network theorists. Network analysis is more amenable to quantitative methods \citep{gibson2005} because much of it is concerned with the effect of social network structures on properties of individuals \citep{Burt2001,Podolny1997}, issues that lend themselves to statistical methods of graphs. In contrast, the study of sequences of social transactions and interaction has traditionally come under the purview of more qualitative research \citep{gibson2005}. Historically, the reason for this has probably been the difficulty to access systematic data-sets of social transactions, precisely because of their ephemeral nature. However, this is now rapidly changing and statistical methods are gradually being applied for the analysis of large transaction data-sets \citep{lazer2009, watts2007}.However, laying the foundations for a project that bridges this divide is intellectually attractive for reasons that were highlighted in the beginning of this chapter, and as we shall see in the following chapters, they are of practical, methodological and theoretical merit. 


To fill this gap in the literature, the `big question' driving this dissertation asks us to identify mechanisms of co-evolution between communication transactions and network structures in the context of email communication. Specifically, we are asked for an empirical account of the links between three levels of analysis: the macro-level of network topology (notions of density, transitivity or even centrality,) the meso-level of the individual and the tie (their properties, for example)  and the micro-level of the individual engaging in social transactions. To get a handle on this big question, the next (methodological) Chapter asks a straightforward and practical question: how should one go about constructing a network model, given a set of digitally mediated transactions?


%What is at stake here is the relation between ties and transactions. A social tie is a group of two individuals. It could simply be defined as the aggregation of all interactions between these two individuals like Homans suggested in the quote above (see page \pageref{quote:Homans}.) But many would claim that a tie is something `over and above' the set of interactions, that in fact these interaction stem from, and contribute to changes in the group, and, as Simmel suggested, they  are not only the facilitators of transactions but could also stop them. There might be some form of `group identity,' a common cause, a purpose and an evolution that are different at the level of the group and the level of the interaction. Here are some of the differences between the transactions and relationships (see ~\ref{tab:ComparingSocialTransactionsAndSocialTies}). First, the scale of transactions is usually taken as relatively localized in time and space whereas social ties are relatively more durable constructs. This observation has two consequences: one regarding how we might study interdependencies. The second is how we might apply a macro-micro explanatory framework to study these two phenomena. 
%
%First, the ephemeral nature of transactions lends them to be interdependent in a sequential manner. For example, email communication, like conversational exchange, consists of chains of related social transactions. Each email may serve as an invitation or stimulus for the next email in the chain, possibly setting in motion a series of related emails that bounce back and forth between actors, sometimes mobilizing more actors in the process. Social ties exist concurrently in a social network, and each of them is rendered more or less probable by the properties of their local neighborhood \citep{Wasserman1996, gibson2005}. 
%
%The different lifetimes of ties and transaction has another theoretical consequence: each tie is associated with multiple transactions, that is, a tie is should be taken analytically at a higher abstraction level than transactions. This raises a subtle point: in general, social events can span multiple actors and multiple ties (Gibson 2000). An utterance, a message or an email, can be seen as a social event in which divides multiple actors into (usually) one source and (potentially) multiple targets. To complicate matters further, each of these targets can take different 'roles'. In an email, some of these targets could be designated in the 'to' field, others in the 'cc' field and still others in the 'bcc' field. However, by definition a social tie binds only two actors. This means that each social event can span multiple ties, and each tie can span multiple events. This N:N association between social ties and social events is not coherent with the mechanism oriented explanations, which require a 1-to-N tie between the macro and micro entities. 
%To solve this problem, the lowest unit of analysis must be identified as that which is common both to the event and to the tie. Going back to the email example, each multi-recipient email must be broken down to the level of the dyad. This is precisely how we can use the term 'transaction' - the breaking down of a (potentially) multi-actor event into its dyadic constituents.   
%
%
%
%\begin{table}[htb]
%	\renewcommand{\arraystretch}{1.5}
%	\centering
%		\begin{tabular}{|l|ll|}
%			\hline
%			      & Social transactions & Social ties \\
%			\hline 
%				Lifetime &  Ephemeral &    Durable \\
%				Type of variable &  Manifest &    Latent \\
%				Embedded in \ldots & Events and Ties & Social networks \\
%				Links & Sequential & Concurrent \\
%				Data collection & observations, archives & Questionnaires, archives \\
%			\hline
%		\end{tabular}  
%	\caption{Comparing social transactions and social ties}
%	\label{tab:ComparingSocialTransactionsAndSocialTies}
%\end{table}
%
%
%



% this big question in the context of email communication transactions, the next chapter identifies some of the distinguishing features of email transactions, and explores what affecth they might have on the network of transactions. 

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